The Russia–Ukraine war disproportionately threatens the nutrition security of developing countries

While the ongoing Russia–Ukraine war threatens global nutrition security, the magnitude and extent of its impact remain underexamined. Here we show that, with the lowest level of war duration, severity, sanction, and countries involved, the direct and indirect impacts of the war and sanctions could newly place 67.3 million people (roughly equals the total population of France) in undernourishment and 316.7 million people (roughly equals the total population of Bangladesh and Russia) suffering from extreme national food insecurity. Approximately 95% of the affected population are from developing countries, highlighting the vulnerability of food supply in these countries. Both the undernourished population and its inequality across countries will substantially grow, if war duration and severity increase. If the war is prolonged to early 2024, future agricultural growth cannot fully offset the negative impacts, and global hunger will still very likely exacerbate. We conclude that targeted measures should be placed in developing countries and their vulnerable populations to reconstruct a just, healthy, and environmentally sustainable food system. Supplementary Information The online version contains supplementary material available at 10.1007/s43621-022-00112-8.

Ukraine brought about by the Russian-Ukrainian war, the duration of the Russian-Ukrainian war, the intensity of sanctions in the non-theater zone against Russia and the number of countries involved. According to this, we can assess the consequences of the Russian-Ukrainian war on global grain trade by considering different war factors and trade sanctions. A detailed description of the model structure, equations, parameters and model simulation is provided below.

Production Function Module
There are many estimation methods for industrial production, such as the Leontief production function 10 , Cobb-Douglas (C-D) function, and Constant Elasticity of Substitution (CES) function 11 . Considering that there is no prediction about the occurrence of a war, and economic agents cannot adjust in time, this study chooses the Leontief production function. Since it does not allow substitution between inputs, it is most suitable for this study.
According to the Leontief function, the output from sector in region ( !,# ) can be expressed in the following equation: Demand activities will be reshaped by the Russian-Ukrainian war.

Capital limitation
Due to the decline in available labor and the tightening of the global supply chain, the capital market has also received a serious impact, hindering production activities, making the capital limitation also one of the bottlenecks in production activities Where ! ,%-( ) refers to the maximum output when the capital market is restricted.
!,# ( ) the primary inputs for the firm at time step .
If we consider the limitations of primary, capital limitation, and intermediate inputs, the maximum production capacity of sector in time is :

Supply constraints
In terms of demand, there is a shortage of food production and supply due to the war.
Hence, the total order demand for the sector in period ( !,# ( )) equals to the sum of intermediate demand and household demand.
The storage of intermediate input at the initial stage to the intermediate input:

Labor Supply Module
War-induced labor constraints could have serious knock-on effects on food production and beyond. In the context of the Russian-Ukrainian war, the inability of employees to work due to death or war constraints is a key factor to consider when assessing impact disasters. In our model, the proportion of surviving productive capacity from the constrained labor productive capacity ( ! 1%' ) after a shock is defined as:

Demand Module
To make a more realistic representation to the real production process, we assume that each sector holds some inventory of intermediate goods.
The actual production will be allocated to downstream economic sectors and households according to their orders. If the output is not enough to meet all orders, the output of a firm will not be able to fulfill all the orders of its clients. A rationing scheme that reflects a mechanism on the basis of which a firm allocates an insufficient amount of products to its clients is needed. Similarly, if the firm's transportation to customers or suppliers is restricted, production will also be affected. For example, during the outbreak of war between Russia-Ukraine, the authorities imposed a strict war blockade.
These measures restrict the supply of labor and the transportation of products. This has led to a reduction in Ukraine's output and has also triggered forward and backward effects.

Food consumption
This section provides supplementary methods on how to calculate food consumption.
Using the multi-region input-output table output by the AMRIO model, we can calculate the weekly total output of the agricultural sector under different war paths: where , , , and G66H represent the identity matrix, technical coefficient matrix, Leontief inverse matrix, and weekly final demand, respectively. After adding up, we can get the total output of the food sector in a year: # N represents the food consumption per unit of output of sector in region before the war (we assume food consumption intensity will not change with war).